In a device such as that discussed in German Patent Application No. 198 26 047 A1, each valve positioner, whose positioning piston may be connected in one piece with the valve tappet of the assigned gas exchange valve, may have its first working chamber continuously connected to a high-pressure source. Each valve positioner may have its second working chamber connected to a first electrical control valve, which alternately closes or releases a supply line to the high-pressure source, and to a second control valve, which alternately closes or releases a relief line. The electrical control valves may be implemented as 2/2 directional-control solenoid valves having spring return. In the event the control valves are without current, the first working chamber may still be under high pressure, while the second working chamber may be disconnected from the high-pressure source and may be connected to the relief line. The gas exchange valve may be closed. To open the gas exchange valve, both control valves may have current applied to them. Through the changeover of the control valves, the second working chamber of the valve positioner may be shut off in relation to the relief line by the second control valve and connected to the high-pressure source by the first control valve using the supply line. The gas exchange valve may open, the size of the opening stroke may be a function of the implementation of the electrical control signal applied to the first electrical control valve and the opening speed may be a function of the pressure introduced from the high-pressure source. In order to keep the gas exchange valve in a specific open position, the first control valve may subsequently be deenergized, so that it may shut off the supply line to the second working chamber of the valve positioner. In this manner, all of the valve opening positions of the gas exchange valve may be set using an electrical control unit for producing control signals. Two electrical control valves, which apply hydraulic pressure to the assigned valve positioner appropriately, may be necessary for controlling each gas exchange valve.